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In the autumn of 2005, Cubberley joined the Elmira College Soaring Eagles. In her freshman season, she accumulated a record of seven wins and two losses. The following season (2006-07), Cubberley sported an impressive 11-3 mark with three shutouts.

Cubberley joined the Burlington Barracudas in 2009, but was released after one season. The Toronto Furies signed her, and she spent the 2010-11 season in a backup capacity to Sami Jo Small. During the 2011-12 CWHL season, Cubberley rejoined the Burlington Barracudas in their final CWHL season.[1] Her Goals Against Average of 4.48 was better than Burlington’s team GAA of 5.56.